Related papers: Self-avoiding walks on scale-free networks
We investigate the properties of a deterministic walk, whose locomotion rule is always to travel to the nearest site. Initially the sites are randomly distributed in a closed rectangular ($A/L \times L)$ landscape and, once reached, they…
A celebrated problem in numerical analysis is to consider Brownian motion originating at the centre of a $10 \times 1$ rectangle, and to evaluate the ratio of probabilities of a Brownian path hitting the short ends of the rectangle before…
We propose a novel Bayesian methodology which uses random walks for rapid inference of statistical properties of undirected networks with weighted or unweighted edges. Our formalism yields high-accuracy estimates of the probability…
A comprehensive numerical study of self-avoiding walks (SAW's) on randomly diluted lattices in two and three dimensions is carried out. The critical exponents $\nu$ and $\chi$ are calculated for various different occupation probabilities,…
We use new algorithms, based on the finite lattice method of series expansion, to extend the enumeration of self-avoiding walks and polygons on the triangular lattice to length 40 and 60, respectively. For self-avoiding walks to length 40…
Random walks can be used to search complex networks for a desired resource. To reduce search lengths, we propose a mechanism based on building random walks connecting together partial walks (PW) previously computed at each network node.…
Complex networks have been studied extensively due to their relevance to many real systems as diverse as the World-Wide-Web (WWW), the Internet, energy landscapes, biological and social networks…
A model for growing networks is introduced, having as a main ingredient that new nodes are attached to the network through one existing node and then explore the network through the links of the visited nodes. From exact calculations of two…
Small-world networks are the focus of recent interest because they appear to circumvent many of the limitations of either random networks or regular lattices as frameworks for the study of interaction networks of complex systems. Here, we…
Counting the number of N-step self-avoiding walks (SAWs) on a lattice is one of the most difficult problems of enumerative combinatorics. Once we give up calculating the exact number of them, however, we have a chance to apply powerful…
We show how the theory of the critical behaviour of $d$-dimensional polymer networks gives a scaling relation for self-avoiding {\em bridges} that relates the critical exponent for bridges $\gamma_b$ to that of terminally-attached…
Our goal is to quickly find top $k$ lists of nodes with the largest degrees in large complex networks. If the adjacency list of the network is known (not often the case in complex networks), a deterministic algorithm to find a node with the…
Unlike the well-studied models of growing networks, where the dominant dynamics consist of insertions of new nodes and connections, and rewiring of existing links, we study {\em ad hoc} networks, where one also has to contend with rapid and…
We introduce and simulate the random walk that adapts move strategies according to local node preferences on a directed graph. We consider graphs with double-hierarchical connectivity and variable wiring diagram in the universality class of…
The cover time of random walks on a graph has found wide practical applications in different fields of computer science, such as crawling and searching on the World Wide Web and query processing in sensor networks, with the application…
Random walk on discrete lattice models is important to understand various types of transport processes. The extreme events, defined as exceedences of the flux of walkers above a prescribed threshold, have been studied recently in the…
Random walks (RWs) are fundamental stochastic processes with applications across physics, computer science, and information processing. A recent extension, the laser chaos decision-maker, employs chaotic time series from semiconductor…
Based on the empirical analysis of the dependency network in 18 Java projects, we develop a novel model of network growth which considers both: an attachment mechanism and the addition of new nodes with a heterogeneous distribution of their…
An analytic effective medium theory is constructed to study the mean access times for random walks on hybrid disordered structures formed by embedding complex networks into regular lattices, considering transition rates $F$ that are…
We give exact relations which are valid for small-world networks (SWN's) with a general `degree distribution', i.e the distribution of nearest-neighbor connections. For the original SWN model, we illustrate how these exact relations can be…